static PetscReal LINPACKcgpthy(PetscReal *a,PetscReal *b)
{
  /* System generated locals */
  PetscReal ret_val,d__1,d__2,d__3;

  /* Local variables */
  PetscReal p,r,s,t,u;

  PetscFunctionBegin;
/*     FINDS DSQRT(A**2+B**2) WITHOUT OVERFLOW OR DESTRUCTIVE UNDERFLOW */


/* Computing MAX */
  d__1 = PetscAbsReal(*a);
  d__2 = PetscAbsReal(*b);
  p    = PetscMax(d__1,d__2);
  if (!p) goto L20;
/* Computing MIN */
  d__2 = PetscAbsReal(*a);
  d__3 = PetscAbsReal(*b);
/* Computing 2nd power */
  d__1 = PetscMin(d__2,d__3) / p;
  r    = d__1 * d__1;
L10:
  t = r + 4.;
  if (t == 4.) goto L20;
  s = r / t;
  u = s * 2. + 1.;
  p = u * p;
/* Computing 2nd power */
  d__1 = s / u;
  r    = d__1 * d__1 * r;
  goto L10;
L20:
  ret_val = p;
  PetscFunctionReturn(ret_val);
} /* cgpthy_ */

PetscErrorCode KSPView_FCG(KSP ksp,PetscViewer viewer)
{
  KSP_FCG        *fcg = (KSP_FCG*)ksp->data;
  PetscErrorCode ierr;
  PetscBool      iascii,isstring;
  const char     *truncstr;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);

  if (fcg->truncstrat == KSP_FCG_TRUNC_TYPE_STANDARD) truncstr = "Using standard truncation strategy";
  else if (fcg->truncstrat == KSP_FCG_TRUNC_TYPE_NOTAY) truncstr = "Using Notay's truncation strategy";
  else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Undefined FCG truncation strategy");

  if (iascii) {
    ierr = PetscViewerASCIIPrintf(viewer,"  FCG: m_max=%D\n",fcg->mmax);CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  FCG: preallocated %D directions\n",PetscMin(fcg->nprealloc,fcg->mmax+1));CHKERRQ(ierr);
    ierr = PetscViewerASCIIPrintf(viewer,"  FCG: %s\n",truncstr);CHKERRQ(ierr);
  } else if (isstring) {
    ierr = PetscViewerStringSPrintf(viewer,"m_max %D nprealloc %D %s",fcg->mmax,fcg->nprealloc,truncstr);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

int main( int argc, char **argv )
{
  PetscErrorCode ierr;
  Mat         	 A;		  /* Grcar matrix */
  SVD            svd;             /* singular value solver context */
  PetscInt    	 N=30, Istart, Iend, i, col[5], nconv1, nconv2;
  PetscScalar 	 value[] = { -1, 1, 1, 1, 1 };
  PetscReal   	 sigma_1, sigma_n;

  SlepcInitialize(&argc,&argv,(char*)0,help);

  ierr = PetscOptionsGetInt(PETSC_NULL,"-n",&N,PETSC_NULL);CHKERRQ(ierr);
  ierr = PetscPrintf(PETSC_COMM_WORLD,"\nEstimate the condition number of a Grcar matrix, n=%d\n\n",N);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
        Generate the matrix 
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
  ierr = MatSetFromOptions(A);CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(A,&Istart,&Iend);CHKERRQ(ierr);
  for( i=Istart; i<Iend; i++ ) {
    col[0]=i-1; col[1]=i; col[2]=i+1; col[3]=i+2; col[4]=i+3;
    if (i==0) {
      ierr = MatSetValues(A,1,&i,4,col+1,value+1,INSERT_VALUES);CHKERRQ(ierr);
    }
    else {
      ierr = MatSetValues(A,1,&i,PetscMin(5,N-i+1),col,value,INSERT_VALUES);CHKERRQ(ierr);
    }
  }

  ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
             Create the singular value solver and set the solution method
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /* 
     Create singular value context
  */
  ierr = SVDCreate(PETSC_COMM_WORLD,&svd);CHKERRQ(ierr);

  /* 
     Set operator
  */
  ierr = SVDSetOperator(svd,A);CHKERRQ(ierr);

  /*
     Set solver parameters at runtime
  */
  ierr = SVDSetFromOptions(svd);CHKERRQ(ierr);
  ierr = SVDSetDimensions(svd,1,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
                      Solve the eigensystem
     - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */

  /*
     First request an eigenvalue from one end of the spectrum
  */
  ierr = SVDSetWhichSingularTriplets(svd,SVD_LARGEST);CHKERRQ(ierr);
  ierr = SVDSolve(svd);CHKERRQ(ierr);
  /* 
     Get number of converged singular values
  */
  ierr = SVDGetConverged(svd,&nconv1);CHKERRQ(ierr);
  /* 
     Get converged singular values: largest singular value is stored in sigma_1.
     In this example, we are not interested in the singular vectors
  */
  if (nconv1 > 0) {
    ierr = SVDGetSingularTriplet(svd,0,&sigma_1,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD," Unable to compute large singular value!\n\n");CHKERRQ(ierr);
  } 

  /*
     Request an eigenvalue from the other end of the spectrum
  */
  ierr = SVDSetWhichSingularTriplets(svd,SVD_SMALLEST);CHKERRQ(ierr);
  ierr = SVDSolve(svd);CHKERRQ(ierr);
  /* 
     Get number of converged eigenpairs
  */
  ierr = SVDGetConverged(svd,&nconv2);CHKERRQ(ierr);
  /* 
     Get converged singular values: smallest singular value is stored in sigma_n. 
     As before, we are not interested in the singular vectors
  */
  if (nconv2 > 0) {
    ierr = SVDGetSingularTriplet(svd,0,&sigma_n,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
  } else {
    ierr = PetscPrintf(PETSC_COMM_WORLD," Unable to compute small singular value!\n\n");CHKERRQ(ierr);
  } 

  /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
                    Display solution and clean up
//.........这里部分代码省略.........

PetscErrorCode KSPFGMRESCycle(PetscInt *itcount,KSP ksp)
{

  KSP_FGMRES     *fgmres = (KSP_FGMRES*)(ksp->data);
  PetscReal      res_norm;
  PetscReal      hapbnd,tt;
  PetscBool      hapend = PETSC_FALSE;  /* indicates happy breakdown ending */
  PetscErrorCode ierr;
  PetscInt       loc_it;                /* local count of # of dir. in Krylov space */
  PetscInt       max_k = fgmres->max_k; /* max # of directions Krylov space */
  Mat            Amat,Pmat;
  MatStructure   pflag;

  PetscFunctionBegin;
  /* Number of pseudo iterations since last restart is the number
     of prestart directions */
  loc_it = 0;

  /* note: (fgmres->it) is always set one less than (loc_it) It is used in
     KSPBUILDSolution_FGMRES, where it is passed to KSPFGMRESBuildSoln.
     Note that when KSPFGMRESBuildSoln is called from this function,
     (loc_it -1) is passed, so the two are equivalent */
  fgmres->it = (loc_it - 1);

  /* initial residual is in VEC_VV(0)  - compute its norm*/
  ierr = VecNorm(VEC_VV(0),NORM_2,&res_norm);CHKERRQ(ierr);

  /* first entry in right-hand-side of hessenberg system is just
     the initial residual norm */
  *RS(0) = res_norm;

  ksp->rnorm = res_norm;
  ierr       = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
  ierr       = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);

  /* check for the convergence - maybe the current guess is good enough */
  ierr = (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
  if (ksp->reason) {
    if (itcount) *itcount = 0;
    PetscFunctionReturn(0);
  }

  /* scale VEC_VV (the initial residual) */
  ierr = VecScale(VEC_VV(0),1.0/res_norm);CHKERRQ(ierr);

  /* MAIN ITERATION LOOP BEGINNING*/
  /* keep iterating until we have converged OR generated the max number
     of directions OR reached the max number of iterations for the method */
  while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
    if (loc_it) {
      ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
      ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
    }
    fgmres->it = (loc_it - 1);

    /* see if more space is needed for work vectors */
    if (fgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
      ierr = KSPFGMRESGetNewVectors(ksp,loc_it+1);CHKERRQ(ierr);
      /* (loc_it+1) is passed in as number of the first vector that should
         be allocated */
    }

    /* CHANGE THE PRECONDITIONER? */
    /* ModifyPC is the callback function that can be used to
       change the PC or its attributes before its applied */
    (*fgmres->modifypc)(ksp,ksp->its,loc_it,res_norm,fgmres->modifyctx);


    /* apply PRECONDITIONER to direction vector and store with
       preconditioned vectors in prevec */
    ierr = KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));CHKERRQ(ierr);

    ierr = PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);CHKERRQ(ierr);
    /* Multiply preconditioned vector by operator - put in VEC_VV(loc_it+1) */
    ierr = MatMult(Amat,PREVEC(loc_it),VEC_VV(1+loc_it));CHKERRQ(ierr);


    /* update hessenberg matrix and do Gram-Schmidt - new direction is in
       VEC_VV(1+loc_it)*/
    ierr = (*fgmres->orthog)(ksp,loc_it);CHKERRQ(ierr);

    /* new entry in hessenburg is the 2-norm of our new direction */
    ierr = VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);CHKERRQ(ierr);

    *HH(loc_it+1,loc_it)  = tt;
    *HES(loc_it+1,loc_it) = tt;

    /* Happy Breakdown Check */
    hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
    /* RS(loc_it) contains the res_norm from the last iteration  */
    hapbnd = PetscMin(fgmres->haptol,hapbnd);
    if (tt > hapbnd) {
      /* scale new direction by its norm */
      ierr = VecScale(VEC_VV(loc_it+1),1.0/tt);CHKERRQ(ierr);
    } else {
      /* This happens when the solution is exactly reached. */
      /* So there is no new direction... */
      ierr   = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr);     /* set VEC_TEMP to 0 */
      hapend = PETSC_TRUE;
    }
//.........这里部分代码省略.........

/*
   FormInitialGuess - Forms initial approximation.

   Input Parameters:
   user - user-defined application context
   X - vector

   Output Parameter:
   X - vector
 */
int FormInitialGuess(AppCtx *user,Vec X)
{
  int         i,j,row,mx,my,ierr;
  PetscReal   one = 1.0,lambda,temp1,temp,hx,hy,hxdhy,hydhx,sc;
  PetscScalar *x;

  /*
      Process 0 has to wait for all other processes to get here
   before proceeding to write in the shared vector
  */
  ierr = PetscBarrier((PetscObject)X);CHKERRQ(ierr);
  if (user->rank) {
    /*
       All the non-busy processors have to wait here for process 0 to finish
       evaluating the function; otherwise they will start using the vector values
       before they have been computed
    */
    ierr = PetscBarrier((PetscObject)X);CHKERRQ(ierr);
    return 0;
  }

  mx = user->mx;               my = user->my;        lambda = user->param;
  hx = one/(PetscReal)(mx-1);  hy = one/(PetscReal)(my-1);
  sc = hx*hy*lambda;        hxdhy = hx/hy;            hydhx = hy/hx;

  temp1 = lambda/(lambda + one);

  /*
     Get a pointer to vector data.
       - For default PETSc vectors, VecGetArray() returns a pointer to
         the data array.  Otherwise, the routine is implementation dependent.
       - You MUST call VecRestoreArray() when you no longer need access to
         the array.
  */
  ierr = VecGetArray(X,&x);CHKERRQ(ierr);

  /*
     Compute initial guess over the locally owned part of the grid
  */
#pragma arl(4)
#pragma distinct (*x,*f)
#pragma no side effects (sqrt)
  for (j=0; j<my; j++) {
    temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
    for (i=0; i<mx; i++) {
      row = i + j*mx;
      if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
        x[row] = 0.0;
        continue;
      }
      x[row] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
    }
  }

  /*
     Restore vector
  */
  ierr = VecRestoreArray(X,&x);CHKERRQ(ierr);

  ierr = PetscBarrier((PetscObject)X);CHKERRQ(ierr);
  return 0;
}

PetscErrorCode VecView_MPI_Draw_DA1d(Vec xin,PetscViewer v)
{
  DM                da;
  PetscErrorCode    ierr;
  PetscMPIInt       rank,size,tag1,tag2;
  PetscInt          i,n,N,step,istart,isize,j,nbounds;
  MPI_Status        status;
  PetscReal         coors[4],ymin,ymax,min,max,xmin = 0.0,xmax = 0.0,tmp = 0.0,xgtmp = 0.0;
  const PetscScalar *array,*xg;
  PetscDraw         draw;
  PetscBool         isnull,showpoints = PETSC_FALSE;
  MPI_Comm          comm;
  PetscDrawAxis     axis;
  Vec               xcoor;
  DMBoundaryType    bx;
  const PetscReal   *bounds;
  PetscInt          *displayfields;
  PetscInt          k,ndisplayfields;
  PetscBool         hold;

  PetscFunctionBegin;
  ierr = PetscViewerDrawGetDraw(v,0,&draw);CHKERRQ(ierr);
  ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
  ierr = PetscViewerDrawGetBounds(v,&nbounds,&bounds);CHKERRQ(ierr);

  ierr = VecGetDM(xin,&da);CHKERRQ(ierr);
  if (!da) SETERRQ(PetscObjectComm((PetscObject)xin),PETSC_ERR_ARG_WRONG,"Vector not generated from a DMDA");

  ierr = PetscOptionsGetBool(NULL,"-draw_vec_mark_points",&showpoints,NULL);CHKERRQ(ierr);

  ierr = DMDAGetInfo(da,0,&N,0,0,0,0,0,&step,0,&bx,0,0,0);CHKERRQ(ierr);
  ierr = DMDAGetCorners(da,&istart,0,0,&isize,0,0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xin,&array);CHKERRQ(ierr);
  ierr = VecGetLocalSize(xin,&n);CHKERRQ(ierr);
  n    = n/step;

  /* get coordinates of nodes */
  ierr = DMGetCoordinates(da,&xcoor);CHKERRQ(ierr);
  if (!xcoor) {
    ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,0.0,0.0,0.0);CHKERRQ(ierr);
    ierr = DMGetCoordinates(da,&xcoor);CHKERRQ(ierr);
  }
  ierr = VecGetArrayRead(xcoor,&xg);CHKERRQ(ierr);

  ierr = PetscObjectGetComm((PetscObject)xin,&comm);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);

  /*
      Determine the min and max x coordinate in plot
  */
  if (!rank) {
    xmin = PetscRealPart(xg[0]);
  }
  if (rank == size-1) {
    xmax = PetscRealPart(xg[n-1]);
  }
  ierr = MPI_Bcast(&xmin,1,MPIU_REAL,0,comm);CHKERRQ(ierr);
  ierr = MPI_Bcast(&xmax,1,MPIU_REAL,size-1,comm);CHKERRQ(ierr);

  ierr = DMDASelectFields(da,&ndisplayfields,&displayfields);CHKERRQ(ierr);
  for (k=0; k<ndisplayfields; k++) {
    j    = displayfields[k];
    ierr = PetscViewerDrawGetDraw(v,k,&draw);CHKERRQ(ierr);
    ierr = PetscDrawCheckResizedWindow(draw);CHKERRQ(ierr);

    /*
        Determine the min and max y coordinate in plot
    */
    min = 1.e20; max = -1.e20;
    for (i=0; i<n; i++) {
      if (PetscRealPart(array[j+i*step]) < min) min = PetscRealPart(array[j+i*step]);
      if (PetscRealPart(array[j+i*step]) > max) max = PetscRealPart(array[j+i*step]);
    }
    if (min + 1.e-10 > max) {
      min -= 1.e-5;
      max += 1.e-5;
    }
    if (j < nbounds) {
      min = PetscMin(min,bounds[2*j]);
      max = PetscMax(max,bounds[2*j+1]);
    }

    ierr = MPI_Reduce(&min,&ymin,1,MPIU_REAL,MPIU_MIN,0,comm);CHKERRQ(ierr);
    ierr = MPI_Reduce(&max,&ymax,1,MPIU_REAL,MPIU_MAX,0,comm);CHKERRQ(ierr);

    ierr = PetscViewerDrawGetHold(v,&hold);CHKERRQ(ierr);
    if (!hold) {
      ierr = PetscDrawSynchronizedClear(draw);CHKERRQ(ierr);
    }
    ierr = PetscViewerDrawGetDrawAxis(v,k,&axis);CHKERRQ(ierr);
    ierr = PetscLogObjectParent((PetscObject)draw,(PetscObject)axis);CHKERRQ(ierr);
    if (!rank) {
      const char *title;

      ierr = PetscDrawAxisSetLimits(axis,xmin,xmax,ymin,ymax);CHKERRQ(ierr);
      ierr = PetscDrawAxisDraw(axis);CHKERRQ(ierr);
      ierr = PetscDrawGetCoordinates(draw,coors,coors+1,coors+2,coors+3);CHKERRQ(ierr);
      ierr = DMDAGetFieldName(da,j,&title);CHKERRQ(ierr);
      if (title) {ierr = PetscDrawSetTitle(draw,title);CHKERRQ(ierr);}
//.........这里部分代码省略.........

PetscErrorCode DMPlexVTKWriteCells_ASCII(DM dm, FILE *fp, PetscInt *totalCells)
{
  MPI_Comm       comm;
  DMLabel        label;
  IS             globalVertexNumbers = NULL;
  const PetscInt *gvertex;
  PetscInt       dim;
  PetscInt       numCorners = 0, totCorners = 0, maxCorners, *corners;
  PetscInt       numCells   = 0, totCells   = 0, maxCells, cellHeight;
  PetscInt       numLabelCells, maxLabelCells, cMax, cStart, cEnd, c, vStart, vEnd, v;
  PetscMPIInt    numProcs, rank, proc, tag;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = PetscCommGetNewTag(comm, &tag);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = DMGetDimension(dm, &dim);CHKERRQ(ierr);
  ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, NULL);CHKERRQ(ierr);
  if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
  ierr = DMPlexGetLabel(dm, "vtk", &label);CHKERRQ(ierr);
  ierr = DMPlexGetStratumSize(dm, "vtk", 1, &numLabelCells);CHKERRQ(ierr);
  ierr = MPI_Allreduce(&numLabelCells, &maxLabelCells, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  if (!maxLabelCells) label = NULL;
  for (c = cStart; c < cEnd; ++c) {
    PetscInt *closure = NULL;
    PetscInt closureSize, value;

    if (label) {
      ierr = DMLabelGetValue(label, c, &value);CHKERRQ(ierr);
      if (value != 1) continue;
    }
    ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    for (v = 0; v < closureSize*2; v += 2) {
      if ((closure[v] >= vStart) && (closure[v] < vEnd)) ++numCorners;
    }
    ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
    ++numCells;
  }
  maxCells = numCells;
  ierr     = MPI_Reduce(&numCells, &totCells, 1, MPIU_INT, MPI_SUM, 0, comm);CHKERRQ(ierr);
  ierr     = MPI_Reduce(&numCells, &maxCells, 1, MPIU_INT, MPI_MAX, 0, comm);CHKERRQ(ierr);
  ierr     = MPI_Reduce(&numCorners, &totCorners, 1, MPIU_INT, MPI_SUM, 0, comm);CHKERRQ(ierr);
  ierr     = MPI_Reduce(&numCorners, &maxCorners, 1, MPIU_INT, MPI_MAX, 0, comm);CHKERRQ(ierr);
  ierr     = DMPlexGetVertexNumbering(dm, &globalVertexNumbers);CHKERRQ(ierr);
  ierr     = ISGetIndices(globalVertexNumbers, &gvertex);CHKERRQ(ierr);
  ierr     = PetscMalloc1(maxCells, &corners);CHKERRQ(ierr);
  ierr     = PetscFPrintf(comm, fp, "CELLS %d %d\n", totCells, totCorners+totCells);CHKERRQ(ierr);
  if (!rank) {
    PetscInt *remoteVertices;
    int      *vertices;

    ierr = PetscMalloc1(maxCorners, &vertices);CHKERRQ(ierr);
    for (c = cStart, numCells = 0; c < cEnd; ++c) {
      PetscInt *closure = NULL;
      PetscInt closureSize, value, nC = 0;

      if (label) {
        ierr = DMLabelGetValue(label, c, &value);CHKERRQ(ierr);
        if (value != 1) continue;
      }
      ierr = DMPlexGetTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      for (v = 0; v < closureSize*2; v += 2) {
        if ((closure[v] >= vStart) && (closure[v] < vEnd)) {
          const PetscInt gv = gvertex[closure[v] - vStart];
          vertices[nC++] = gv < 0 ? -(gv+1) : gv;
        }
      }
      ierr = DMPlexRestoreTransitiveClosure(dm, c, PETSC_TRUE, &closureSize, &closure);CHKERRQ(ierr);
      corners[numCells++] = nC;
      ierr = PetscFPrintf(comm, fp, "%d ", nC);CHKERRQ(ierr);
      ierr = DMPlexInvertCell(dim, nC, vertices);CHKERRQ(ierr);
      for (v = 0; v < nC; ++v) {
        ierr = PetscFPrintf(comm, fp, " %d", vertices[v]);CHKERRQ(ierr);
      }
      ierr = PetscFPrintf(comm, fp, "\n");CHKERRQ(ierr);
    }
    if (numProcs > 1) {ierr = PetscMalloc1(maxCorners+maxCells, &remoteVertices);CHKERRQ(ierr);}
    for (proc = 1; proc < numProcs; ++proc) {
      MPI_Status status;

      ierr = MPI_Recv(&numCorners, 1, MPIU_INT, proc, tag, comm, &status);CHKERRQ(ierr);
      ierr = MPI_Recv(remoteVertices, numCorners, MPIU_INT, proc, tag, comm, &status);CHKERRQ(ierr);
      for (c = 0; c < numCorners;) {
        PetscInt nC = remoteVertices[c++];

        for (v = 0; v < nC; ++v, ++c) {
          vertices[v] = remoteVertices[c];
        }
        ierr = DMPlexInvertCell(dim, nC, vertices);CHKERRQ(ierr);
        ierr = PetscFPrintf(comm, fp, "%d ", nC);CHKERRQ(ierr);
        for (v = 0; v < nC; ++v) {
          ierr = PetscFPrintf(comm, fp, " %d", vertices[v]);CHKERRQ(ierr);
        }
        ierr = PetscFPrintf(comm, fp, "\n");CHKERRQ(ierr);
      }
//.........这里部分代码省略.........

//.........这里部分代码省略.........
  ierr = MatGetOwnershipRanges(A,(const PetscInt**)&mat_ranges);CHKERRQ(ierr);
  for (i=0;i<nsubdomains;i++) {
    for (j=mat_ranges[i];j<mat_ranges[i+1];j++) {
      row_ownership[j] = i;
    }
  }

  /*
     my_dnz and my_onz contains exact contribution to preallocation from each local mat
     then, they will be summed up properly. This way, preallocation is always sufficient
  */
  ierr = PetscCalloc2(local_rows,&my_dnz,local_rows,&my_onz);CHKERRQ(ierr);
  /* preallocation as a MATAIJ */
  if (isdense) { /* special case for dense local matrices */
    for (i=0;i<local_rows;i++) {
      PetscInt index_row = global_indices_r[i];
      for (j=i;j<local_rows;j++) {
        PetscInt owner = row_ownership[index_row];
        PetscInt index_col = global_indices_c[j];
        if (index_col > mat_ranges[owner]-1 && index_col < mat_ranges[owner+1] ) { /* diag block */
          my_dnz[i] += 1;
        } else { /* offdiag block */
          my_onz[i] += 1;
        }
        /* same as before, interchanging rows and cols */
        if (i != j) {
          owner = row_ownership[index_col];
          if (index_row > mat_ranges[owner]-1 && index_row < mat_ranges[owner+1] ) {
            my_dnz[j] += 1;
          } else {
            my_onz[j] += 1;
          }
        }
      }
    }
  } else { /* TODO: this could be optimized using MatGetRowIJ */
    for (i=0;i<local_rows;i++) {
      const PetscInt *cols;
      PetscInt       ncols,index_row = global_indices_r[i];
      ierr = MatGetRow(matis->A,i,&ncols,&cols,NULL);CHKERRQ(ierr);
      for (j=0;j<ncols;j++) {
        PetscInt owner = row_ownership[index_row];
        PetscInt index_col = global_indices_c[cols[j]];
        if (index_col > mat_ranges[owner]-1 && index_col < mat_ranges[owner+1] ) { /* diag block */
          my_dnz[i] += 1;
        } else { /* offdiag block */
          my_onz[i] += 1;
        }
        /* same as before, interchanging rows and cols */
        if (issbaij && index_col != index_row) {
          owner = row_ownership[index_col];
          if (index_row > mat_ranges[owner]-1 && index_row < mat_ranges[owner+1] ) {
            my_dnz[cols[j]] += 1;
          } else {
            my_onz[cols[j]] += 1;
          }
        }
      }
      ierr = MatRestoreRow(matis->A,i,&ncols,&cols,NULL);CHKERRQ(ierr);
    }
  }
  ierr = ISLocalToGlobalMappingRestoreIndices(A->rmap->mapping,&global_indices_r);CHKERRQ(ierr);
  if (global_indices_c != global_indices_r) {
    ierr = ISLocalToGlobalMappingRestoreIndices(A->rmap->mapping,&global_indices_c);CHKERRQ(ierr);
  }
  ierr = PetscFree(row_ownership);CHKERRQ(ierr);

  /* Reduce my_dnz and my_onz */
  if (maxreduce) {
    ierr = PetscSFReduceBegin(matis->sf,MPIU_INT,my_dnz,dnz,MPI_MAX);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(matis->sf,MPIU_INT,my_dnz,dnz,MPI_MAX);CHKERRQ(ierr);
    ierr = PetscSFReduceBegin(matis->sf,MPIU_INT,my_onz,onz,MPI_MAX);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(matis->sf,MPIU_INT,my_onz,onz,MPI_MAX);CHKERRQ(ierr);
  } else {
    ierr = PetscSFReduceBegin(matis->sf,MPIU_INT,my_dnz,dnz,MPI_SUM);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(matis->sf,MPIU_INT,my_dnz,dnz,MPI_SUM);CHKERRQ(ierr);
    ierr = PetscSFReduceBegin(matis->sf,MPIU_INT,my_onz,onz,MPI_SUM);CHKERRQ(ierr);
    ierr = PetscSFReduceEnd(matis->sf,MPIU_INT,my_onz,onz,MPI_SUM);CHKERRQ(ierr);
  }
  ierr = PetscFree2(my_dnz,my_onz);CHKERRQ(ierr);

  /* Resize preallocation if overestimated */
  for (i=0;i<lrows;i++) {
    dnz[i] = PetscMin(dnz[i],lcols);
    onz[i] = PetscMin(onz[i],cols-lcols);
  }
  /* set preallocation */
  ierr = MatMPIAIJSetPreallocation(B,0,dnz,0,onz);CHKERRQ(ierr);
  for (i=0;i<lrows/bs;i++) {
    dnz[i] = dnz[i*bs]/bs;
    onz[i] = onz[i*bs]/bs;
  }
  ierr = MatMPIBAIJSetPreallocation(B,bs,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatMPISBAIJSetPreallocation(B,bs,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatPreallocateFinalize(dnz,onz);CHKERRQ(ierr);
  if (issbaij) {
    ierr = MatRestoreRowUpperTriangular(matis->A);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/***********************************ivec.c*************************************/
PetscErrorCode PCTFS_ivec_min( PetscInt *arg1,  PetscInt *arg2,  PetscInt n)
{
  PetscFunctionBegin;
  while (n--)  {*(arg1) = PetscMin(*arg1,*arg2); arg1++; arg2++;}
  PetscFunctionReturn(0);
}

PetscErrorCode EPSSolve_Arnoldi(EPS eps)
{
  PetscErrorCode     ierr;
  PetscInt           k,nv,ld;
  Mat                U;
  PetscScalar        *H,*X;
  PetscReal          beta,gamma=1.0;
  PetscBool          breakdown,harmonic,refined;
  BVOrthogRefineType orthog_ref;
  EPS_ARNOLDI        *arnoldi = (EPS_ARNOLDI*)eps->data;

  PetscFunctionBegin;
  ierr = DSGetLeadingDimension(eps->ds,&ld);CHKERRQ(ierr);
  ierr = DSGetRefined(eps->ds,&refined);CHKERRQ(ierr);
  harmonic = (eps->extraction==EPS_HARMONIC || eps->extraction==EPS_REFINED_HARMONIC)?PETSC_TRUE:PETSC_FALSE;
  ierr = BVGetOrthogonalization(eps->V,NULL,&orthog_ref,NULL);CHKERRQ(ierr);

  /* Get the starting Arnoldi vector */
  ierr = EPSGetStartVector(eps,0,NULL);CHKERRQ(ierr);

  /* Restart loop */
  while (eps->reason == EPS_CONVERGED_ITERATING) {
    eps->its++;

    /* Compute an nv-step Arnoldi factorization */
    nv = PetscMin(eps->nconv+eps->mpd,eps->ncv);
    ierr = DSSetDimensions(eps->ds,nv,0,eps->nconv,0);CHKERRQ(ierr);
    ierr = DSGetArray(eps->ds,DS_MAT_A,&H);CHKERRQ(ierr);
    if (!arnoldi->delayed) {
      ierr = EPSBasicArnoldi(eps,PETSC_FALSE,H,ld,eps->nconv,&nv,&beta,&breakdown);CHKERRQ(ierr);
    } else SETERRQ(PetscObjectComm((PetscObject)eps),1,"Not implemented");
    /*if (orthog_ref == BV_ORTHOG_REFINE_NEVER) {
      ierr = EPSDelayedArnoldi1(eps,H,ld,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);
    } else {
      ierr = EPSDelayedArnoldi(eps,H,ld,eps->V,eps->nconv,&nv,f,&beta,&breakdown);CHKERRQ(ierr);
    }*/
    ierr = DSRestoreArray(eps->ds,DS_MAT_A,&H);CHKERRQ(ierr);
    ierr = DSSetState(eps->ds,DS_STATE_INTERMEDIATE);CHKERRQ(ierr);
    ierr = BVSetActiveColumns(eps->V,eps->nconv,nv);CHKERRQ(ierr);

    /* Compute translation of Krylov decomposition if harmonic extraction used */
    if (harmonic) {
      ierr = DSTranslateHarmonic(eps->ds,eps->target,beta,PETSC_FALSE,NULL,&gamma);CHKERRQ(ierr);
    }

    /* Solve projected problem */
    ierr = DSSolve(eps->ds,eps->eigr,eps->eigi);CHKERRQ(ierr);
    ierr = DSSort(eps->ds,eps->eigr,eps->eigi,NULL,NULL,NULL);CHKERRQ(ierr);
    ierr = DSUpdateExtraRow(eps->ds);CHKERRQ(ierr);

    /* Check convergence */
    ierr = EPSKrylovConvergence(eps,PETSC_FALSE,eps->nconv,nv-eps->nconv,beta,gamma,&k);CHKERRQ(ierr);
    if (refined) {
      ierr = DSGetArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
      ierr = BVMultColumn(eps->V,1.0,0.0,k,X+k*ld);CHKERRQ(ierr);
      ierr = DSRestoreArray(eps->ds,DS_MAT_X,&X);CHKERRQ(ierr);
      ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
      ierr = BVMultInPlace(eps->V,U,eps->nconv,nv);CHKERRQ(ierr);
      ierr = MatDestroy(&U);CHKERRQ(ierr);
      ierr = BVOrthogonalizeColumn(eps->V,k,NULL,NULL,NULL);CHKERRQ(ierr);
    } else {
      ierr = DSGetMat(eps->ds,DS_MAT_Q,&U);CHKERRQ(ierr);
      ierr = BVMultInPlace(eps->V,U,eps->nconv,nv);CHKERRQ(ierr);
      ierr = MatDestroy(&U);CHKERRQ(ierr);
    }
    eps->nconv = k;

    ierr = EPSMonitor(eps,eps->its,eps->nconv,eps->eigr,eps->eigi,eps->errest,nv);CHKERRQ(ierr);
    if (breakdown && k<eps->nev) {
      ierr = PetscInfo2(eps,"Breakdown in Arnoldi method (it=%D norm=%g)\n",eps->its,(double)beta);CHKERRQ(ierr);
      ierr = EPSGetStartVector(eps,k,&breakdown);CHKERRQ(ierr);
      if (breakdown) {
        eps->reason = EPS_DIVERGED_BREAKDOWN;
        ierr = PetscInfo(eps,"Unable to generate more start vectors\n");CHKERRQ(ierr);
      }
    }
    if (eps->its >= eps->max_it) eps->reason = EPS_DIVERGED_ITS;
    if (eps->nconv >= eps->nev) eps->reason = EPS_CONVERGED_TOL;
  }

  /* truncate Schur decomposition and change the state to raw so that
     PSVectors() computes eigenvectors from scratch */
  ierr = DSSetDimensions(eps->ds,eps->nconv,0,0,0);CHKERRQ(ierr);
  ierr = DSSetState(eps->ds,DS_STATE_RAW);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode SNESDiffParameterCompute_More(SNES snes,void *nePv,Vec x,Vec p,double *fnoise,double *hopt)
{
  DIFFPAR_MORE   *neP = (DIFFPAR_MORE*)nePv;
  Vec            w, xp, fvec;    /* work vectors to use in computing h */
  double         zero = 0.0, hl, hu, h, fnoise_s, fder2_s;
  PetscScalar    alpha;
  PetscScalar    fval[7], tab[7][7], eps[7], f = -1;
  double         rerrf = -1., fder2;
  PetscErrorCode ierr;
  PetscInt       iter, k, i, j,  info;
  PetscInt       nf = 7;         /* number of function evaluations */
  PetscInt       fcount;
  MPI_Comm       comm;
  FILE           *fp;
  PetscBool      noise_test = PETSC_FALSE;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr);
  /* Call to SNESSetUp() just to set data structures in SNES context */
  if (!snes->setupcalled) {ierr = SNESSetUp(snes);CHKERRQ(ierr);}

  w    = neP->workv[0];
  xp   = neP->workv[1];
  fvec = neP->workv[2];
  fp   = neP->fp;

  /* Initialize parameters */
  hl       = zero;
  hu       = zero;
  h        = neP->h_first_try;
  fnoise_s = zero;
  fder2_s  = zero;
  fcount   = neP->function_count;

  /* We have 5 tries to attempt to compute a good hopt value */
  ierr = SNESGetIterationNumber(snes,&i);CHKERRQ(ierr);
  ierr = PetscFPrintf(comm,fp,"\n ------- SNES iteration %D ---------\n",i);CHKERRQ(ierr);
  for (iter=0; iter<5; iter++) {
    neP->h_first_try = h;

    /* Compute the nf function values needed to estimate the noise from
       the difference table */
    for (k=0; k<nf; k++) {
      alpha = h * (k+1 - (nf+1)/2);
      ierr  = VecWAXPY(xp,alpha,p,x);CHKERRQ(ierr);
      ierr  = SNESComputeFunction(snes,xp,fvec);CHKERRQ(ierr);
      neP->function_count++;
      ierr = VecDot(fvec,w,&fval[k]);CHKERRQ(ierr);
    }
    f = fval[(nf+1)/2 - 1];

    /* Construct the difference table */
    for (i=0; i<nf; i++) tab[i][0] = fval[i];

    for (j=0; j<6; j++) {
      for (i=0; i<nf-j; i++) {
        tab[i][j+1] = tab[i+1][j] - tab[i][j];
      }
    }

    /* Print the difference table */
    ierr = PetscFPrintf(comm,fp,"Difference Table: iter = %D\n",iter);CHKERRQ(ierr);
    for (i=0; i<nf; i++) {
      for (j=0; j<nf-i; j++) {
        ierr = PetscFPrintf(comm,fp," %10.2e ",tab[i][j]);CHKERRQ(ierr);
      }
      ierr = PetscFPrintf(comm,fp,"\n");CHKERRQ(ierr);
    }

    /* Call the noise estimator */
    ierr = SNESNoise_dnest_(&nf,fval,&h,fnoise,&fder2,hopt,&info,eps);CHKERRQ(ierr);

    /* Output statements */
    rerrf = *fnoise/PetscAbsScalar(f);
    if (info == 1) {ierr = PetscFPrintf(comm,fp,"%s\n","Noise detected");CHKERRQ(ierr);}
    if (info == 2) {ierr = PetscFPrintf(comm,fp,"%s\n","Noise not detected; h is too small");CHKERRQ(ierr);}
    if (info == 3) {ierr = PetscFPrintf(comm,fp,"%s\n","Noise not detected; h is too large");CHKERRQ(ierr);}
    if (info == 4) {ierr = PetscFPrintf(comm,fp,"%s\n","Noise detected, but unreliable hopt");CHKERRQ(ierr);}
    ierr = PetscFPrintf(comm,fp,"Approximate epsfcn %g  %g  %g  %g  %g  %g\n",(double)eps[0],(double)eps[1],(double)eps[2],(double)eps[3],(double)eps[4],(double)eps[5]);CHKERRQ(ierr);
    ierr = PetscFPrintf(comm,fp,"h = %g, fnoise = %g, fder2 = %g, rerrf = %g, hopt = %g\n\n",(double)h, (double)*fnoise, (double)fder2, (double)rerrf, (double)*hopt);CHKERRQ(ierr);

    /* Save fnoise and fder2. */
    if (*fnoise) fnoise_s = *fnoise;
    if (fder2) fder2_s = fder2;

    /* Check for noise detection. */
    if (fnoise_s && fder2_s) {
      *fnoise = fnoise_s;
      fder2   = fder2_s;
      *hopt   = 1.68*sqrt(*fnoise/PetscAbsScalar(fder2));
      goto theend;
    } else {

      /* Update hl and hu, and determine new h */
      if (info == 2 || info == 4) {
        hl = h;
        if (hu == zero) h = 100*h;
        else            h = PetscMin(100*h,0.1*hu);
      } else if (info == 3) {
        hu = h;
//.........这里部分代码省略.........

PetscErrorCode DMPlexVTKWriteSection_ASCII(DM dm, PetscSection section, PetscSection globalSection, Vec v, FILE *fp, PetscInt enforceDof, PetscInt precision, PetscReal scale)
{
  MPI_Comm           comm;
  const MPI_Datatype mpiType = MPIU_SCALAR;
  PetscScalar        *array;
  PetscInt           numDof = 0, maxDof;
  PetscInt           numLabelCells, cellHeight, cMax, cStart, cEnd, numLabelVertices, vMax, vStart, vEnd, pStart, pEnd, p;
  PetscMPIInt        numProcs, rank, proc, tag;
  PetscBool          hasLabel;
  PetscErrorCode     ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  PetscValidHeaderSpecific(dm,DM_CLASSID,1);
  PetscValidHeaderSpecific(v,VEC_CLASSID,4);
  if (precision < 0) precision = 6;
  ierr = PetscCommGetNewTag(comm, &tag);CHKERRQ(ierr);
  ierr = MPI_Comm_size(comm, &numProcs);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm, &rank);CHKERRQ(ierr);
  ierr = PetscSectionGetChart(section, &pStart, &pEnd);CHKERRQ(ierr);
  /* VTK only wants the values at cells or vertices */
  ierr = DMPlexGetVTKCellHeight(dm, &cellHeight);CHKERRQ(ierr);
  ierr = DMPlexGetHeightStratum(dm, cellHeight, &cStart, &cEnd);CHKERRQ(ierr);
  ierr = DMPlexGetDepthStratum(dm, 0, &vStart, &vEnd);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, &cMax, NULL, NULL, &vMax);CHKERRQ(ierr);
  if (cMax >= 0) cEnd = PetscMin(cEnd, cMax);
  if (vMax >= 0) vEnd = PetscMin(vEnd, vMax);
  pStart   = PetscMax(PetscMin(cStart, vStart), pStart);
  pEnd     = PetscMin(PetscMax(cEnd,   vEnd),   pEnd);
  ierr     = DMPlexGetStratumSize(dm, "vtk", 1, &numLabelCells);CHKERRQ(ierr);
  ierr     = DMPlexGetStratumSize(dm, "vtk", 2, &numLabelVertices);CHKERRQ(ierr);
  hasLabel = numLabelCells > 0 || numLabelVertices > 0 ? PETSC_TRUE : PETSC_FALSE;
  for (p = pStart; p < pEnd; ++p) {
    /* Reject points not either cells or vertices */
    if (((p < cStart) || (p >= cEnd)) && ((p < vStart) || (p >= vEnd))) continue;
    if (hasLabel) {
      PetscInt value;

      if (((p >= cStart) && (p < cEnd) && numLabelCells) ||
          ((p >= vStart) && (p < vEnd) && numLabelVertices)) {
        ierr = DMPlexGetLabelValue(dm, "vtk", p, &value);CHKERRQ(ierr);
        if (value != 1) continue;
      }
    }
    ierr = PetscSectionGetDof(section, p, &numDof);CHKERRQ(ierr);
    if (numDof) break;
  }
  ierr = MPI_Allreduce(&numDof, &maxDof, 1, MPIU_INT, MPI_MAX, comm);CHKERRQ(ierr);
  enforceDof = PetscMax(enforceDof, maxDof);
  ierr = VecGetArray(v, &array);CHKERRQ(ierr);
  if (!rank) {
    char formatString[8];

    ierr = PetscSNPrintf(formatString, 8, "%%.%de", precision);CHKERRQ(ierr);
    for (p = pStart; p < pEnd; ++p) {
      /* Here we lose a way to filter points by keeping them out of the Numbering */
      PetscInt dof, off, goff, d;

      /* Reject points not either cells or vertices */
      if (((p < cStart) || (p >= cEnd)) && ((p < vStart) || (p >= vEnd))) continue;
      if (hasLabel) {
        PetscInt value;

        if (((p >= cStart) && (p < cEnd) && numLabelCells) ||
            ((p >= vStart) && (p < vEnd) && numLabelVertices)) {
          ierr = DMPlexGetLabelValue(dm, "vtk", p, &value);CHKERRQ(ierr);
          if (value != 1) continue;
        }
      }
      ierr = PetscSectionGetDof(section, p, &dof);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(section, p, &off);CHKERRQ(ierr);
      ierr = PetscSectionGetOffset(globalSection, p, &goff);CHKERRQ(ierr);
      if (dof && goff >= 0) {
        for (d = 0; d < dof; d++) {
          if (d > 0) {
            ierr = PetscFPrintf(comm, fp, " ");CHKERRQ(ierr);
          }
          ierr = PetscFPrintf(comm, fp, formatString, PetscRealPart(array[off+d])*scale);CHKERRQ(ierr);
        }
        for (d = dof; d < enforceDof; d++) {
          ierr = PetscFPrintf(comm, fp, " 0.0");CHKERRQ(ierr);
        }
        ierr = PetscFPrintf(comm, fp, "\n");CHKERRQ(ierr);
      }
    }
    for (proc = 1; proc < numProcs; ++proc) {
      PetscScalar *remoteValues;
      PetscInt    size = 0, d;
      MPI_Status  status;

      ierr = MPI_Recv(&size, 1, MPIU_INT, proc, tag, comm, &status);CHKERRQ(ierr);
      ierr = PetscMalloc1(size, &remoteValues);CHKERRQ(ierr);
      ierr = MPI_Recv(remoteValues, size, mpiType, proc, tag, comm, &status);CHKERRQ(ierr);
      for (p = 0; p < size/maxDof; ++p) {
        for (d = 0; d < maxDof; ++d) {
          if (d > 0) {
            ierr = PetscFPrintf(comm, fp, " ");CHKERRQ(ierr);
          }
          ierr = PetscFPrintf(comm, fp, formatString, PetscRealPart(remoteValues[p*maxDof+d])*scale);CHKERRQ(ierr);
        }
//.........这里部分代码省略.........

static PetscErrorCode DMPlexVTKWriteAll_ASCII(DM dm, PetscViewer viewer)
{
  MPI_Comm                 comm;
  PetscViewer_VTK          *vtk = (PetscViewer_VTK*) viewer->data;
  FILE                     *fp;
  PetscViewerVTKObjectLink link;
  PetscSection             coordSection, globalCoordSection;
  PetscLayout              vLayout;
  Vec                      coordinates;
  PetscReal                lengthScale;
  PetscInt                 vMax, totVertices, totCells;
  PetscBool                hasPoint = PETSC_FALSE, hasCell = PETSC_FALSE, writePartition = PETSC_FALSE;
  PetscErrorCode           ierr;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)dm,&comm);CHKERRQ(ierr);
  ierr = PetscFOpen(comm, vtk->filename, "wb", &fp);CHKERRQ(ierr);
  ierr = PetscFPrintf(comm, fp, "# vtk DataFile Version 2.0\n");CHKERRQ(ierr);
  ierr = PetscFPrintf(comm, fp, "Simplicial Mesh Example\n");CHKERRQ(ierr);
  ierr = PetscFPrintf(comm, fp, "ASCII\n");CHKERRQ(ierr);
  ierr = PetscFPrintf(comm, fp, "DATASET UNSTRUCTURED_GRID\n");CHKERRQ(ierr);
  /* Vertices */
  ierr = DMPlexGetScale(dm, PETSC_UNIT_LENGTH, &lengthScale);CHKERRQ(ierr);
  ierr = DMGetCoordinateSection(dm, &coordSection);CHKERRQ(ierr);
  ierr = PetscSectionCreateGlobalSection(coordSection, dm->sf, PETSC_FALSE, PETSC_FALSE, &globalCoordSection);CHKERRQ(ierr);
  ierr = DMGetCoordinatesLocal(dm, &coordinates);CHKERRQ(ierr);
  ierr = DMPlexGetHybridBounds(dm, NULL, NULL, NULL, &vMax);CHKERRQ(ierr);
  if (vMax >= 0) {
    PetscInt pStart, pEnd, p, localSize = 0;

    ierr = PetscSectionGetChart(globalCoordSection, &pStart, &pEnd);CHKERRQ(ierr);
    pEnd = PetscMin(pEnd, vMax);
    for (p = pStart; p < pEnd; ++p) {
      PetscInt dof;

      ierr = PetscSectionGetDof(globalCoordSection, p, &dof);CHKERRQ(ierr);
      if (dof > 0) ++localSize;
    }
    ierr = PetscLayoutCreate(PetscObjectComm((PetscObject)dm), &vLayout);CHKERRQ(ierr);
    ierr = PetscLayoutSetLocalSize(vLayout, localSize);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(vLayout, 1);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(vLayout);CHKERRQ(ierr);
  } else {
    ierr = PetscSectionGetPointLayout(PetscObjectComm((PetscObject)dm), globalCoordSection, &vLayout);CHKERRQ(ierr);
  }
  ierr = PetscLayoutGetSize(vLayout, &totVertices);CHKERRQ(ierr);
  ierr = PetscFPrintf(comm, fp, "POINTS %d double\n", totVertices);CHKERRQ(ierr);
  ierr = DMPlexVTKWriteSection_ASCII(dm, coordSection, globalCoordSection, coordinates, fp, 3, PETSC_DETERMINE, lengthScale);CHKERRQ(ierr);
  /* Cells */
  ierr = DMPlexVTKWriteCells_ASCII(dm, fp, &totCells);CHKERRQ(ierr);
  /* Vertex fields */
  for (link = vtk->link; link; link = link->next) {
    if ((link->ft == PETSC_VTK_POINT_FIELD) || (link->ft == PETSC_VTK_POINT_VECTOR_FIELD)) hasPoint = PETSC_TRUE;
    if ((link->ft == PETSC_VTK_CELL_FIELD)  || (link->ft == PETSC_VTK_CELL_VECTOR_FIELD))  hasCell  = PETSC_TRUE;
  }
  if (hasPoint) {
    ierr = PetscFPrintf(comm, fp, "POINT_DATA %d\n", totVertices);CHKERRQ(ierr);
    for (link = vtk->link; link; link = link->next) {
      Vec          X = (Vec) link->vec;
      DM           dmX;
      PetscSection section, globalSection, newSection = NULL;
      const char   *name;
      PetscInt     enforceDof = PETSC_DETERMINE;

      if ((link->ft != PETSC_VTK_POINT_FIELD) && (link->ft != PETSC_VTK_POINT_VECTOR_FIELD)) continue;
      if (link->ft == PETSC_VTK_POINT_VECTOR_FIELD) enforceDof = 3;
      ierr = PetscObjectGetName(link->vec, &name);CHKERRQ(ierr);
      ierr = VecGetDM(X, &dmX);CHKERRQ(ierr);
      if (dmX) {
        DMLabel  subpointMap, subpointMapX;
        PetscInt dim, dimX, pStart, pEnd, qStart, qEnd;

        ierr = DMGetDefaultSection(dmX, &section);CHKERRQ(ierr);
        /* Here is where we check whether dmX is a submesh of dm */
        ierr = DMGetDimension(dm,  &dim);CHKERRQ(ierr);
        ierr = DMGetDimension(dmX, &dimX);CHKERRQ(ierr);
        ierr = DMPlexGetChart(dm,  &pStart, &pEnd);CHKERRQ(ierr);
        ierr = DMPlexGetChart(dmX, &qStart, &qEnd);CHKERRQ(ierr);
        ierr = DMPlexGetSubpointMap(dm,  &subpointMap);CHKERRQ(ierr);
        ierr = DMPlexGetSubpointMap(dmX, &subpointMapX);CHKERRQ(ierr);
        if (((dim != dimX) || ((pEnd-pStart) < (qEnd-qStart))) && subpointMap && !subpointMapX) {
          const PetscInt *ind = NULL;
          IS              subpointIS;
          PetscInt        n = 0, q;

          ierr = PetscSectionGetChart(section, &qStart, &qEnd);CHKERRQ(ierr);
          ierr = DMPlexCreateSubpointIS(dm, &subpointIS);CHKERRQ(ierr);
          if (subpointIS) {
            ierr = ISGetLocalSize(subpointIS, &n);CHKERRQ(ierr);
            ierr = ISGetIndices(subpointIS, &ind);CHKERRQ(ierr);
          }
          ierr = PetscSectionCreate(comm, &newSection);CHKERRQ(ierr);
          ierr = PetscSectionSetChart(newSection, pStart, pEnd);CHKERRQ(ierr);
          for (q = qStart; q < qEnd; ++q) {
            PetscInt dof, off, p;

            ierr = PetscSectionGetDof(section, q, &dof);CHKERRQ(ierr);
            if (dof) {
              ierr = PetscFindInt(q, n, ind, &p);CHKERRQ(ierr);
              if (p >= pStart) {
//.........这里部分代码省略.........

/*
   PCGAMGCreateGraph - create simple scaled scalar graph from matrix

 Input Parameter:
 . Amat - matrix
 Output Parameter:
 . a_Gmaat - eoutput scalar graph (symmetric?)
 */
PetscErrorCode PCGAMGCreateGraph(Mat Amat, Mat *a_Gmat)
{
  PetscErrorCode ierr;
  PetscInt       Istart,Iend,Ii,jj,kk,ncols,nloc,NN,MM,bs;
  MPI_Comm       comm;
  Mat            Gmat;
  MatType        mtype;

  PetscFunctionBegin;
  ierr = PetscObjectGetComm((PetscObject)Amat,&comm);CHKERRQ